The invention relates to a surface acoustic wave (SAW) device useful in band-limited TV systems, and suitable for carrier-compatible chirp-Z transform Fourier analysis. It includes apparatus for taking the discrete Fourier transform of a complex input signal using a SAW chirp generator, fed by a pulse generator, which generates two mutually orthogonal, sine and cosine components. Two bandpass filters are generally required, whose outputs are connected to the input of a SAW chirp filter. Two low-pass filters at the output of the device are required, one to filter the real component and the other to filter the imaginary component of the transformed complex input signal.
Prior art devices for computing the discrete Fourier transform (DFT) of an input signal using the chirp-Z transform (CZT) algorithm have relied upon a sampled format for filter, multiplier, and signal representations. They usually operated at baseband.
Such a system calculates an N-point transform via circular convolution over (2N-1) sample intervals. Thus, a pair of such systems operating "in parallel" is required to perform continuous-duty operation. Circular convolution for the CZT structure is usually accomplished in one of two ways: (a) recirculate the data back through an N-tap filter just after the Nth sample is first entered, or (b) cycle N input samples just once through a (2N-1) -tap filter whose last (N-taps are a replication of the first (N-1) taps.